If \(A\subseteq B\), then \(A\cap B\) is equal to which set?
Answer and explanation
Correct answer: \(A\)
Because \(A\subseteq B\), every element of \(A\) is also an element of \(B\). The intersection contains elements common to both sets, so it contains every element of \(A\) and no element outside \(A\) is required. Therefore, \(A\cap B=A\). Set \(B\) may have additional elements, the union is generally larger, and \(B\setminus A\) contains elements of \(B\) excluded from \(A\).
Frequently asked questions
What is the correct answer to this question?
\(A\)
Why is this the correct answer?
Because \(A\subseteq B\), every element of \(A\) is also an element of \(B\). The intersection contains elements common to both sets, so it contains every element of \(A\) and no element outside \(A\) is required. Therefore, \(A\cap B=A\). Set \(B\) may have additional elements, the union is generally larger, and \(B\setminus A\) contains elements of \(B\) excluded from \(A\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
